SOLUTION: Good Morning, Can anyone show me the steps for this, please? Consider the following equation and determine if it is a parabola, an ellipse, or a hyperbola and sketch it's graph:

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Question 968527: Good Morning, Can anyone show me the steps for this, please?
Consider the following equation and determine if it is a parabola, an ellipse, or a hyperbola and sketch it's graph:
4y^2+6x−2y+3x^2−15=2y^2+4x^2
Thank you in advance for your help.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!

Does this solution process contain a mistake?



Complete The Squares for x and y






Possible mistake but at least steps still lead to hyperbola with vertex on the y axis but not on the x-axis.

Sign mistake, MAYBE made.
A way to avoid that, if it actually happened, could be to start with all x on one side and all y on the other side, and then perform Completion of the Squares.











-----Without checking through a solution a third time, this one is probably correct for less likely to have made arithmetic mistakes.
Still hyperbola with vertices on the y axis IF were in a form centered at the origin; but this one is centered at ( 7, 1/2 ).
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Good Morning, Can anyone show me the steps for this, please?
Consider the following equation and determine if it is a parabola, an ellipse, or a hyperbola and sketch it's graph:
4y^2+6x−2y+3x^2−15=2y^2+4x^2
Thank you in advance for your help.
After combining like-terms, it's obvious that the leading coefficients (+ 1 and - 2) have different signs. 

Therefore, it's a . 

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